Bautista, M.A.

Deprince, Jérome

Fritzsche, S.

Garcia, J.

Kallman, T.R.

Mendoza, C.

Palmeri, Patrick

Quinet, Pascal

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Received: 22 November 2018 Revised: 15 February 2019 Accepted: 4 March 2019DOI: 10.1002/xrs.3040S P E C I A L I S S U EK-line X-ray fluorescence from highly charged iron ionsunder dense astrophysical plasma conditionsJérôme Deprince1 Manuel Bautista2 Stephan Fritzsche3,4 Javier García5Timothy Kallman6 Claudio Mendoza2 Patrick Palmeri1 Pascal Quinet1,71Physique Atomique et Astrophysique,Université de Mons, Mons B-7000,Belgium2Department of Physics, Western MichiganUniversity, Kalamazoo 4908, MI, USA3Helmholtz Institut Jena, Jena 07743,Germany4Theoretisch Physikalisches Institut,Friedrich Schiller Universität Jena, 07743Jena, Germany5Department of Astronomy, CaliforniaInstitute of Technology, Pasadena 91125,CA, USA6NASA Goddard Space Flight Center,Code 662, Greenbelt, MD, USA7IPNAS, Université de Liège, B-4000Liège, BelgiumCorrespondenceJérôme Deprince, Physique Atomique etAstrophysique, Université de Mons, MonsB-7000, Belgium.Email: jerome.deprince@umons.ac.beFunding informationNASA, Grant/Award Number:APRA15-0114In the present work, we report an investigation of plasma environment effectson the atomic parameters associated with the K-vacancy states in highly chargediron ions within the astrophysical context of accretion disks around black holes.More particularly, the sensitivity of K-line X-ray fluorescence parameters (wave-lengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXVions has been estimated for plasma conditions characterized by an electron tem-perature ranging from 105 to 107 K and an electron density ranging from 1018 to1022 cm−3. In order to do this, relativistic multiconfiguration Dirac-Fock atomicstructure calculations have been carried out by considering a time averagedDebye-Hückel potential for both the electron–nucleus and electron–electroninteractions.1 INTRODUCTIONIn the inner-radius region of a black-hole accretion disk,high plasma densities (≥ 1020 cm−3) are likely to exist.[1]This would affect all atomic parameters, either by chang-ing the atomic structures and associated rates or by low-ering the ionization potentials, increasing the importanceof collisional processes. It is, therefore, imperative thatmodels of X-ray spectra from astrophysical sources includeplasma environment effects in the atomic data. Address-ing the problem of high-density plasma is important also inmodeling other astrophysical media such as the accretiondisks of neutron stars, the atmospheres of white dwarfs,and partially ionized outflows from galactic black holes.[2]In these X-ray sources, the plasma densities approach orexceed the limits of applicability for many of the rates incurrent atomic databases[1]; thus, new atomic calculationstailored for high density plasmas are urgently needed. Inthis context, the importance of K-shell atomic processeshas been appreciated since the launch of X-ray observato-ries Chandra and XMM-Newton. In particular, iron K linesemitted by accretion disks around black holes are widelyused to investigate Doppler and gravitational effects andto measure the black-hole spin.[3] However, the accuracyof these spin estimates is called into question because themodels used to determine those parameters from observa-X-Ray Spectrometry. 2019;1–4. wileyonlinelibrary.com/journal/xrs © 2019 John Wiley & Sons, Ltd. 12 DEPRINCE ET AL.tions require inexplicably large iron abundances, severaltimes the solar value (Garcia[4] and references therein).The most likely explanation for these iron overabundancesis a deficiency in the models, and the main reason might bethat current models are inapplicable at densities above 1018cm−3. Recently, we have started a systematic investigationof plasma environment effects on the K-line parameters iniron ions.[5,6] In the present paper, we focus on the calcu-lation of K-edge energies, line wavelengths, fluorescenceyields, and natural level widths in three particular ions,that is, Fe XVII, Fe XVIII, and Fe XIX, under plasma con-ditions characterized by an electron temperature rangingfrom 105 to 107 K and an electron density ranging from 1018to 1022 cm−3.2 THEORETICAL APPROACHThe atomic structure calculations were carried out byusing the fully relativistic multiconfiguration Dirac-Fockmethod,[7] as implemented in the GRASP92[8] andRATIP[9] codes. In this approach, each atomic statefunction is represented as a linear combination of con-figuration state functions of the same parity (P) and totalangular momentum (J,M) :|||Ψ𝛼(PJM) >=nc∑k=1ck(𝛼)|||𝛾kPJM >, (1)where the configuration state functions are antisym-metrized products of a common set of orthonormalorbitals, which are optimized self-consistently based onthe Dirac-Coulomb HamiltonianHDC =∑ihD(ri) +∑i>𝑗1ri𝑗, (2)with the one-electron Dirac operator, hD.In order to model the effects of the plasma screening onthe atomic properties, we used a Debye-Hückel potential.This technique has already been used in several studies toTABLE 1 Computed level energies, fluorescence yields, and natural widths for K-vacancystates in Fe XVII–XIX ions as a function of the plasma screening parameter 𝜇, in a.uEnergy (keV) 𝝎k (s−1) Γk (eV)Ion Level 𝜇 = 0.0 𝜇 = 0.25 𝜇 = 0.0 𝜇 = 0.25 𝜇 = 0.0 𝜇 = 0.25Fe XVII 1s2s22p63s 3S1 7.151 7.143 0.44 0.44 5.70 5.661s2s22p63s 1S0 7.156 7.148 0.43 0.43 5.90 5.851s2s22p63p 3P0 7.183 7.176 0.44 0.45 5.66 5.581s2s22p63p 3P1 7.184 7.176 0.45 0.45 5.46 5.381s2s22p63p 3P2 7.186 7.179 0.46 0.46 5.46 5.421s2s22p63p 1P1 7.190 7.182 0.49 0.50 5.89 5.83Fe XVIII 1s2s22p6 2S1/2 6.437 6.435 0.29 0.29 8.86 8.75Fe XIX 1s2s22p5 3P2 6.470 6.468 0.34 0.35 5.07 5.021s2s22p5 3P1 6.477 6.474 0.38 0.38 5.28 5.231s2s22p5 3P0 6.485 6.482 0.35 0.35 4.98 4.941s2s22p5 1P1 6.497 6.495 0.51 0.51 6.34 6.301s2s2p6 3S1 6.587 6.585 0.45 0.45 5.75 5.711s2s2p6 1S0 6.615 6.613 0.36 0.36 7.33 7.24FIGURE 1 Variation of the radiative (left panel) and Auger (right panel) rates with the plasma screening parameter for the K-vacancy1s2s22p63p text3P0 state in Fe XVIIDEPRINCE ET AL. 3simulate the plasma environment (see, e.g., Sahaet al.[10–12]). This model potential reads, in atomic units(a.u.), asV DH(r, 𝜇) = −N∑iZe−𝜇riri+N∑i>𝑗e−𝜇ri𝑗ri𝑗, (3)where N is the number of bound electrons, ri is the dis-tance of the ith electron from the nucleus, and rij is thedistancebetweentheelectrons i and j.Moreover, theplasmascreening parameter,𝜇, is the inverse of the Debye shieldinglength, 𝜆De, and can be expressed in terms of the elec-tron density, ne, and temperature, Te, of the plasma as(in a.u.)𝜇 = 1𝜆De=√4𝜋nekTe. (4)Hence, any given values of both the temperature andthe electron density of the plasma correspond to a certainvalue of the screening parameter 𝜇. In the astrophysi-cal context of an accretion disk around black hole, thephysical conditions can be expected to be such as Te =105 – 107 K and ne = 1018 – 1022 cm−3, which correspondsto screening parameter values up to about 0.25 a.u. Conse-quently, in our work, the plasma environment effects wereestimated by means of a Debye-Hückel potential with ascreening parameter 𝜇 ranging from 0 (isolated ion case) to0.25 a.u.3 RESULTS AND DISCUSSION3.1 Fluorescence yields and natural levelwidthsFor a K-vacancy level (i.e., a level belonging to a configura-tion with one hole in the K-shell), k, the fluorescence yield,𝜔k and the natural width, Γk, are respectively given by𝜔k =∑i Arki∑i Arki + Aak, (5)andΓk =∑iArki + Aak, (6)where Arki represents the radiative transition probability tothe lower level i, and Aak is the Auger rate.The 𝜔k and 𝛤k values calculated in our work forK-vacancy states in Fe XVII–Fe XIX using two differentplasma screening parameters, that is, 𝜇 = 0 and 0.25 a.u.,are reported in Table 1. It is clear that the influence of theplasma environment on the results is rather small, the fluo-rescence yields being unchanged whereas the natural levelwidths appear to systematically decrease (by 1% on aver-age), although the changes in radiative and Auger ratesdo not exhibit any systematic trend. This is illustrated inFigure 1 where the behaviour of some calculated Ar andAa values in Fe XVII is plotted against the plasma screen-ing parameter. We also note from Table 1 that the energiesof K-vacancy level are lowered by about 8, 2, and 3 eV, inFe XVII, Fe XVIII, and Fe XIX, respectively.TABLE 2 Computed K-edge energies, in keV, for Fe XVII–XIXions as a function of the plasma screening parameter 𝜇, in a.uIon 𝜇 = 0.0 𝜇 = 0.25 ShiftFe XVII 7.698 7.582 −0.116Fe XVIII 7.827 7.705 −0.122Fe XIX 7.960 7.831 −0.129FIGURE 2 Variation of the calculated wavelengths with the plasma screening parameter (𝜇 = 0 a.u. in black; 𝜇 = 0.25 a.u. in red) for thestrongest K𝛼 lines in Fe XVII4 DEPRINCE ET AL.3.2 K-edge energies and emission linewavelengthsThe K-edge energy is set by the binding energy of theK-shell electrons of an atomic system. The effects of theplasma environment on the K-edge energies in Fe XVII, FeXVIII, and Fe XIX are shown in Table 2. They are reducedby 116, 122, and 129 eV, respectively, when going from𝜇 = 0 to 𝜇 = 0.25 a.u. This lowering could change theX-ray spectrum and the identification of those ions, whichis often based on the position of the K-edges. The wave-lengths computed in our work using 𝜇 = 0 and 0.25 a.u.are compared in Figure 2 for emission K lines in Fe XVII.They all appear to be redshifted by about 1 mÅ.ACKNOWLEDGEMENTSJ. D. is a Research Fellow of the Belgian Fund for ResearchTraining in Industry and Agriculture (FRIA). P. P. andP. Q. are, respectively, Research Associate and ResearchDirector of the Belgian Fund for Scientific Research(F.R.S.-FNRS). Financial support from these organiza-tions, as well as from the NASA (grant APRA15-0114), wasgratefully acknowledged.ORCIDJérôme Deprince https://orcid.org/0000-0002-3409-8232REFERENCES[1] J. D. Schnittman, J. H. Krolik, S. C. Noble, Astrophys. J. 2013,769, 156.[2] J. M. Miller, A. C. Fabian, J. Kaastra, T. Kallman, A. L. King, D.Proga, J. Raymond, C. S. Reynolds, Astrophys. J. 2015, 814, 87.[3] J. M. Miller, Annu. Rev. Astron. Astrophys. 2007, 45, 441.[4] J. Garcia, T. Kallman, M. A. Bautista, C. Mendoza, J. Deprince,P. Palmeri, P. Quinet, Astron. Soc. Pacific Conf. Ser. 2018, 515,282.[5] J. Deprince, S. Fritzsche, T. Kallman, P. Palmeri, P. Quinet, Can.J. Phys. 2017, 95, 858.[6] J. Deprince, S. Fritzsche, T. R. Kallman, P. Palmeri, P. Quinet,in AIP Conf. Proc., 1811 2017, 040002.[7] I. P. Grant, Relativistic Quantum Theory of Atoms and Molecules,Springer, New York 2007.[8] F. A. Parpia, C. Froese Fischer, I. P. Grant, Comput. Phys.Commun. 1996, 94, 249.[9] S. Fritzsche, Comput. Phys. Commun. 2012, 183, 1525.[10] B. Saha, S. Fritzsche, Phys. Rev. E. 2006, 73, 036405.[11] J. K. Saha, S. Bhattacharyya, T. K. Mukherjee, P. K. Mukherjee,J. Phys. B. At., Mol. Opt. Phys. 2009, 42, 24.[12] M. Das, B. K. Sahoo, S. Pal, Phys. Rev. A. 2016, 93, 052513.How to cite this article: Deprince J, Bautista M,Fritzsche S, et al. K-line X-ray fluorescence fromhighly charged iron ions under dense astrophysicalplasma conditions. X-Ray Spectrometry. 2019;1–4.https://doi.org/10.1002/xrs.3040

K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions

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K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions

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